Forest stand density and stocking : concepts, terms, and the use of stocking guides

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Forest Stand Density
and Stocking: Concepts,
Terms, and The Use
of Stocking Guides

Introduction

In this report we discuss the standardization of the eoneepts ami
terms of stocking and stand density. We also consider the use of
stocking guides, especially the Gingrich guide.1 Both the terminol-
ogy and this guide have been adopted by the USDA Forest Service
National Forest System and the Timber Management Research
Stall, although research continues on new and better expressions
of stand density.

The attempt to standardize stocking has long been a source of
confusion and controversy among foresters, despite efforts to clar-
ify the situation (Bickford and others 1957). Curtis (1970)
identified basic relationships among a number of stand density
measures, and his analysis unified the interpretation of many of
these measures. MacLcan (1979) made further distinctions and
clarifications in terminology as applied to the Pacific Northwest
Forest Survey. All these were admirable attempts to bring some
meaningful criteria into the field.

'This name is incorrectly spelled "Ginrich" in the citation on page 7. In
ull other instances in this publication the correct spelling is used.

For we must remember that the development of standards in the
matters of stocking and stand density arc not of casual interest.
They arc vital to the performance of the work that we have
undertaken. Such standards arc implicitly demanded in the man-
date that we have from Congress, in the National Forest Manage-
ment Act of 1976, section 4(d)( I ). ". . . It is the policy of Congress
that all forested lands in the National Forest System shall be main-
tained in appropriate forest cover with species of trees, degree of
stocking, rate of growth, and conditions of stand designed to se-
cure the maximum benefits of multiple use sustained yield man-
agement in accordance with land management plans." (USDA FS
1983) The carrying out of this law requires the development, on a
national level, of a standardized concept of stocking and a consist-
ent interpretation, visualization, and application of stocking
standards.

1

Definitions

To foster a common understanding and interpretation of stock-
ing, it is first necessary to define the terminology and concepts
used. The following definitions of stand density and stocking are
recognized by the Society of American Foresters (1971):

Stand density — A quantitative measure of tree stocking ex-
pressed either relatively as a coefficient, taking normal num-
bers, basal area, or volume (from yield table data) as unity;
or absolutely, in terms of number of trees, total basal area,
or total volume per unit area.

Stocking — A loose term for the amount of anything on a
given area, particularly in relation to what is considered the
optimum.

Many foresters use these two terms interchangeably, but there
are distinct differences. We will maintain consistency with these
recognized definitions and will further clarify and interpret them.
Also, in this publication, we are going to define other significant
concepts and terms. Six of the most important are as follows:

• Absolute stand density — the absolute or measured quantity
per unit area (that is, trees per acre or square feet per acre).

• Management zone — the area defined by the upper and
lower bounds of acceptable relative densities in stands man-
aged for a particular objective.

• Reference level — the absolute stand density that we would
normally expect in a stand of given characteristics under
some standard condition (usually average maximum compe-
tition, but may be no competition).

• Relative stand density derived from average maximum
competition — the ratio (proportion or percent) of absolute
stand density to the reference level based on average maxi-
mum competition.

• Relative stand density derived from no competition — the

ratio (proportion or percent) of absolute stand density to the
reference level based on no competition.

• Stocking level — a residual stand density, expressed as rela-
tive stand density, that achieves some management
objective.

Stand density: some aspects

In the following discussion, we will assess density only in in-
dividual forest stands that have grown beyond the seedling-
sapling stage. The term "stocking" can be used in a number of
contexts. For example, stocking adequacy can be evaluated at
several points in the life of a stand. The methods used during the
early years are meant to evaluate the adequacy of the regenera-
tion stocking. These methods differ from those used in later years
when overstory stand density is evaluated. In this report we are
concerned primarily with evaluating overstory density and devel-
oping standards for overstory stocking. (Those methods, how-
ever, that deal with regeneration stocking should always take
care that the stand, as it matures, will ultimately fall within the

desired management zone.)

It has long been recognized that intensive management of the
forest resource can increase the yield of usable products over the
rotation of the stand. Controlling stand density is a primary
mechanism for controlling stand growth. In reviewing European
thinning practices, Braathe (1957) stated:

... In European thinnings, the best possible future develop-
ment of the stand is the main principle. . . . This is best
achieved by the free thinning method, which leaves a suita-
ble number of the best trees as evenly spaced as possible
over the area. . . . The height growth is little affected by
thinning on good sites within the density interval used in
practice. ... On the other hand, diameter growth is greatly
stimulated by thinnings, especially in the lower part of the
trunk, producing larger dimensions in shorter time.

It is generally accepted that gross stand volume growth is
fairly constant over a considerable range of stand densities, but
net stand growth (gross growth less mortality) may decrease as
stand density increases. Despite nearly constant gross stand
volume increment, we thin to salvage the anticipated volume lost
to mortality, and to put the volume increment onto fewer (and
hopefully bigger and more desirable) trees in larger increments.
Through intermediate thinnings we can control density and in-
crease the total return from the stand over the rotation. When
thinning, the question is how much material should be removed
and how much should remain. Establishing stocking standards is
an attempt to answer that question and to help the manager make
sound decisions about treating the stand.

In a simplistic conception of the impact of stand density on
growth, there are finite amounts of resources available in any
given area for tree growth. If we start with a single tree on a plot,
that tree would have all of the resources it could use, and excess
resources would be available for other vegetation. We could add
additional trees to the plot (increasing the stand density), and
each would have all the resources it could use. But as the number
of trees on the plot increases, inter-tree competition begins, and
eventually a point is reached where all resources for growth are
used. This is the point of full site utilization. As the number of
trees on the plot further increases, the competition among the
trees for light, moisture, and nutrients also increases.

Growth of individual trees in open stands will be at a maxi-
mum (within the limits imposed by other factors): however, total
stand growth will be less than maximum. Stand growth increases
with increasing numbers of trees, but at a decreasing rate since
the growth of individual trees is reduced by increasing competi-
tion among trees. Above the point of full site utilization, growth
of individual trees decreases as stand density increases, while to-
tal gross stand growth remains nearly constant. Mortality also in-
creases as stand density increases because some individual trees
would no longer have the minimum amount of resources required
to survive.

When thinning, we manipulate stand density to capitalize on
these growth responses. The primary objectives of thinning are to
(1) salvage the material that otherwise would have died, thereby
increasing total yields over the rotation: (2) increase the growth
rate on individual trees selected to be retained: (3) improve qual-
ity and species composition: and (4) maintain stand health.

2

Stocking levels are the recommended residual relative stand den
sities that capitalize on these responses to best meet a specific
management objective. (Management objectives will be dis-
cussed in more detail in a later section of this publication.)
Absolute stand density lor Stands of the same age, species

composition, structure, and site is meaningful lor purposes ol

comparison. When any or all of these stand characteristics
change, comparison of absolute stand density becomes less
meaningful. For example, it is a natural tendency lor the basal
area per unit area to increase and the number of trees per unit
area to decrease as the stand grows older. Since these absolute
measures change over time, meaningful comparisons among
stands must include some measure of average tree size or stage of

stand development

The concept of relative stand density has been developed to
provide meaningful comparisons among stands that differ in av-
erage tree size, age, site, and associated characteristics. Relative
stand density is the ratio of the measured absolute density of a
given stand to some reference level specific to that forest type. It
describes the "degree of crowding" in the stand When the evalu-
ation of two stands results in the same relative stand density, they
can be thought of as being at the same degree of crowding, even
though they may differ in age, stand size, or species composi-
tion. This ability to measure and compare the degree of crowding
is extremely valuable

3

Stand density: reference levels

Two reference levels to measure stand density have been
widely used. These levels must be determined biologically; and,
as Curtis (1971) describes them, they may be either a level of av-
erage maximum competition or a level of no competition. The
former is the more common and probably the more useful refer-
ence level. Note that some writers have used the biological maxi-
mum; this defines the extreme upper limit of density and is dis-
tinct from the average of many high-density stands. Average
maximum competition is based on the absolute density observed
in undisturbed stands of the same type and size, often referred to
as "normal" stands in older American yield tables. The A-level in
Gingrich's (1967) oak stocking guide and the maximum density
lines of Reineke (1933) and Drew and Flewelling (1979) are ex-
amples of reference levels based on average maximum competi-
tion or an estimated upper limit of competition proportional to
this average maximum. Measures such as Chisman and
Schumacher's (1940) tree-area ratio, Reineke's (1933) stand den-
sity index, Curtis' (1982) RD. and Drew and Flewelling's (1977,
1979) relative density measure express stand density relative to
such maximum density levels for stands of the same diameter
(the most common measure) or some other measure of stand
development.

The "no competition" reference level, 100 crown competition
factor (100 CCF), is based on the observed relationship between
crown area and diameter at breast height (d.b.h.) of open-grown
trees. Crown width and d.b.h. are measured on trees that have
developed without competition. The reference level is then de-
fined by the number per unit area (acre or hectare) of such trees

of a given diameter for which the sum of predicted crown areas is
one unit area (acre or hectare). This is the point of crown closure
of a hypothetical stand of uniformly distributed trees of the same
diameter, with crown areas equal to those of open-grown trees of
this diameter. The B-level line of the oak stocking guide, as de-
veloped from the crown competition factor (Krajicek et al.
1961), is an example of a reference level based on such a hypo-
thetical stand. The "no competition" reference level is particu-
larly useful in forest types where factors other than light are lim-
iting, and the closed forest condition often used to identify stands
where average maximum competition cannot often be found.

The choice of a reference level is critical, regardless of the
standard of competition used as reference, because stocking lev-
els are expressed in terms of that standard. A reference level
would be unity or 100 percent, since it is what we expect in natu-
ral undisturbed stands. The crowding (or density) of any stand
can be expressed in relation to the reference level as relative
stand density, as a proportion or percent.

Because, in the past, there have been two reference levels
from which relative density could be calculated, the definition of
relative density may often be ambiguous. The reference level
used should be specified. Since the most common and useful ref-
erence level is average maximum competition, we use the un-
qualified term "relative density" to denote stand density relative
to average maximum competition. If the reference level used is
"no competition," this should be stated explicitly. Only one ref-
erence level should be defined for a forest type.

4

Stocking levels and management objectives

Use of stocking guides

Stocking level implies a managemenl objective. This is distinct
from stand density. A stocking level is the residual relative stand
density that satisfies a management objective, and stocking is ex-
pressed as relative stand density. For example, optimum stand
volume production may occur at .1 Stocking level that is 60 pel
cent of the average maximum competition reference level, or at a
relative stand density of 60 percent.

Stocking levels that satisfy individual management objectives
can be distinctly different: however, they are all expressed as rel-
ative stand density. When stand density is manipulated, the ob-
served biological responses are the basis lor defining a number of
residual density levels. These levels include, but are not limited
to. the levels that achieve:

• Maximum d.b.h. growth of individual trees.

• Maximum volume (or basal area) growth of stands.

• Maximum development of regeneration.

• Maximum development of understory wildlife food.

• Maximum seed production.

• Minimum or acceptable levels of windthrow.

• Minimum or acceptable levels of damage by insects and
diseases.

• Minimum or acceptable bole degrade.

Two considerations are important in making an appropriate
management decision: the biological response of the stand to a
treatment and the economic factors. Biologically, undisturbed
stands show a consistent pattern of development and tend to re-
spond to a given treatment in a consistent way. Economically,
the viability of a treatment depends on accessibility, markets,
utilization standards, and other exogenous variables. The eco-
nomic conditions, particularly markets, are by nature dy-
namic— what is true today might not be tomorrow. Appropriate
management strategies are determined from the biological devel-
opment and responses as constrained by the economic realities.

Any number of stocking levels can be established, each satis-
fying one or more management goals. The establishment of
stocking levels should have long-term research support, and as
research results accumulate, these stocking levels can be dis-
played more accurately on the guides that are drawn up.

Although an optimal residual density may be defined, strict
maintenance of that level would require continuous cutting.
There is a practical limit to the frequency of cutting in a stand,
and it is based on economic returns. Generally, there would be a
lower density limit below which stand production suffers, and an
upper limit above which stand vigor deteriorates. As a result, a
range of residual relative densities is implied as being acceptable.
This range can be thought of as the management zone.

Stocking guides have been developed for most of the major
forest types and species in North America. Many of these guides
express stand density as easily derived field estimates ol the hori-
zontal dimensions of a stand (that is. number of trees and/or ba-
sal area per unit area). Standardization of definitions associated
with these guides, and of the format in which they are presented,
is desirable in order to ensure a common understanding and inter-
pretation of information, regardless of species type.

Several formats for such guides were exaamincd, including
those showing growing-stock levels for ponderosa pine (Myers
1967), natural stand relationships in Douglas-fir (Reukema and
Bruce 1977), and stocking charts for eastern hardwoods
(Gingrich 1967, Roach 1977. Leak et al. 1969). The displays
drawn on these formats arc founded on equations based on
growing space requirements. Curtis (1970 and 1971) pointed out
the functional relationships among them.

The important underlying concept for all of these guides is that
a site has a biologic density potential. When a given stand is
compared to this reference potential, the result is a measure of
relative stand density. Regardless of the formulation used, the
end result is a measure of crowding.

The Gingrich guide

Guides meant to express stocking levels have ranged from a
simple plotting of number of trees or basal area by stand size to
transformed scales and multiple dimensions. An approach devel-
oped by Gingrich (1967) has been used widely to show stand
characteristics. This Gingrich guide has been adopted as the Na-
tional Forest system's standard for stocking guides because of its
simplicity and ease of use.

Some guides use only basal area or number of trees to show
density. Gingrich's design uses both and because of this, infor-
mation from other guides that use either basal area or number of
trees can be transferred to this one format. The design of the
Gingrich guide also aids in visualizing the dynamics of stand
growth and the interactions of basal area and number of trees as a
stand matures.

Gingrich's guide displays the stand basal area, the number of
trees, and the quadratic mean diameter. These parameters are
mathematically related and specification of any two implies the
third. Both basal area per unit area (or the equivalent, sum of di-
ameters squared times a constant) and number of trees per unit
area are easily derived from a field cruise. The quadratic mean
diameter (or the diameter of the tree of average basal area) is
used as a measure of stand size. The mathematically derived
interrelationships between them are shown in figure 1 . the rec-
ommended background chart on which all the stocking levels can
be plotted. Stocking guides that plot only two of these parameters
(such as number of trees by stand size or basal area by stand size)
can easily have their information transferred to this more compre-
hensive design. The basic form of the chart can be developed and
used for any tree species or forest type. Of course, the reference
level and stocking levels fitted to the chart will be specific to the
species, plant community, forest type, habitat type, and manage-
ment objectives.

Because of the need of some organizations for metric equiva-
lents, stocking guides should be developed with both English and

5

metric units of measure. (To avoid confusion, this should be
done through duplicate charts rather than the use of dual scales.)
You may find it helpful to refer to a drawing of the Gingrich
stocking guide (fig. 1) when reading the following sections.

Reference and stocking levels

It is not our purpose to standardize the techniques used in devel-
oping stocking guides. Nor do we recommend that there be only
one reference level for all forest or habitat types, with stocking
levels established on the basis of a single reference level. Rather,
each forest type^would have a unique reference level with appro-
priate stocking levels developed for specific economic conditions.

Much research has been directed toward establishing reference
levels and stocking levels for many forest types, but additional re-
search is needed on other forest types. Where the necessary infor-
mation is available, developing a standardized stocking guide
merely requires transferring the existing information to the format
of the Gingrich guide. Where such information is lacking, consid-
erable effort will be required. This should follow the recommended
procedure that begins on page 7.

The major task in developing a stocking guide is establishing the
reference level for stand density. A variety of techniques have
been used. Curtis (1970) suggested that many of these techniques
can be interpreted as expressions of average area requirements per
tree under the specified conditions of the reference level. West
(1982) also compared many of these measures and pointed out the
advantages of some. Regardless of the methods used, the end re-
sult is the same — a measure of the expected basal area or number

of trees for a stand of given size, composition, and structure under
the specified condition of the reference level. Stands of similar
size, composition, and structure can be compared to this level for a
measure of relative density. Specific formulations of reference lev-
els are detailed in the literature.

The information shown on the Gingrich (1967) stocking guide
includes basal area, number of trees, and diameter of the tree of
mean basal area. These parameters are easily derived from a field
cruise, and relative stand density can then be read from the guide.
The Gingrich stocking guide format as presented on this page is
quick and easy to use.

An alternate and equivalent determination of relative stand den-
sity can be made. If the calculation of average maximum density is
based on equations that indicate growing-space requirements, the
contribution of each tree to relative stand density can be summed
across the stand. Since the growing-space equations were devel-
oped for a specified reference condition, the calculation results in a
measure of stand density relative to that reference level. The com-
putation usually can be reduced to fairly simple equations easily
evaluated for any given stand table.

Methods of determination based on either the chart or on the
summation of growing-space requirements of individual trees, will
result in an equivalent measure of relative stand density. A com-
parison with established stocking levels would then indicate the de-
sirability of a thinning to better meet the management objective.

To develop a stocking level, a management objective must be
determined. The recommended residual density (or stocking level)
and the timing of stand treatments may differ for each objective.
Developing a stocking level requires many long-term measure-

Basal area — ft2 acre

400-

350-

300'

250-

200—

150-

100—

50

24

Quadratic mean diameter

4

Average

maximum density

Upper level of
management zone

Lower level of management zone

Reference level of no competition — 100 CCF

200 400 600 800 1000 1200

Trees per acre

1400

1600

1800

2000

Figure 1 — The Gingrich guide.

6

mcnts of biological responses to the manipulation oi stand density
Slocking levels can be derived through simulation or direct analy-
sis of the data, but either approach requires many experiments and
trials in sample stands. In some forest types, detailed data are no)
available, and guides must be made on the basis ol the best infoi
mation available.

Procedure

The following procedure outlines the steps required in devel
oping stocking guides. There is a great amount of work required to
develop these guides; fortunately, some of this work may already
be completed. Interim stocking guides are needed for species or
types where data are not available. On-going consultation with ami
support from local research organizations such as universities or
Forest Service research laboratories is important.

Step 1: Developing a reference level The reference level can
be based on a standard of average maximum competition or no
competition. The necessary data to develop this level depends on
the standard that is selected. For a standard of no competition,
crown width/d.b.h. equations often arc available. If not, the basic
data needed for each species are measurements of d.b.h. and
crown width of trees grown in an open condition, and they must be
collected over the entire range of diameters usually encountered.
An equation of maximum crown area by diameter is developed
from these data. Karjicek et al. (1961) outline these procedures in
detail.

For a standard of average maximum competition, several meth-
ods already have been discussed. Growing-space allocation tech-
niques are useful and result in reliable measures of stand density.
The basic data needed are stand tables for all trees in a sample of
stands. The stands selected for analysis should be undisturbed,
even-aged, and natural; and should represent a range of age
classes. Tree tallies should include all trees in the stand; trees as
small as 1 inch d.b.h. should be counted where they make up a
significant portion of the stand. Some data of this kind are avail-
able or can be adapted from reliable yield tables. An expression of
growing-space requirements can then be developed. Mathematical
procedures for deriving the necessary equations are found in
Gingrich (1967), Chisman and Schumacher (1940). Curtis (1971),
Reinekc (1933), and West (1982).

Step 2: The stocking guide format After the data are obtained
for the reference level, these data must be adapted into a form in
which they can be used to determine the relative stand density of
sampled stands. Developing a standard chart in the format of fig-
ure 1 entails solving the reference-level equation over a range of
average stand sizes and plotting the solutions in the appropriate
format. For types where this basic work already has been done but
displayed differently, the data generally can be transformed easily
into the standard chart format.

It also may be useful to Fit (if necessary) the reference-level
equations into a form in which they can be applied directly to

sample stand data to derive the measure of relative stand density.
Depending on the procedure used to decide on the reference level
and the type of diameter distribution encountered in the particular
forest type, one may need to modify the expression for average
stand size. Gingrich (1967) and Rogers (1980) include an example
of a type for which such a modification was required.

Step 3: Developing stocking levels Developing stocking levels
is a long-term project. Biological growth responses to the manipu-
lation of stand density must be monitored over long periods in
plots controlled at various residual stand densities. In addition to
volume responses, quality responses also can be monitored, partic-
ularly where high-quality sawtimber is a goal. Growth models de-
veloped from these data can be used to evaluate and select the re-
sidual densities that best meet the management objective for
different economic conditions. Growth response also can be used
to simulate alternative mangement strategies. Stocking levels de-
veloped for a specific forest type may indicate the treatments for
similar forest types for which we have no stocking guides.

Stocking levels can be placed on the chart, stated mathematic-
ally, or stated narratively. For example, maximum volume produc-
tion might occur at a known, specific residual relative density; this
may be dependent on variables such as age stand or on previous
management practices.

Step 4: Drawing up the stocking guide Each stocking guide
should be drawn up in the Gingrich format and should include no-
tations as to the origins of its data. The following information
should be included:

• Species composition or forest type and geographic area of
applicability.

• Definitions of the reference standard (as one of average maxi-
mum competition or some other standard).

• Equations for the reference level where available; sources of
data and procedures of analysis should be documented.

• Placement of the upper and lower stocking levels for the
specified management objective, and the management zone
between. The management objective should be stated
explicitly.

Step 5: Using the guides Comparing the actual relative density
to the recommended relative density may imply an opportunity for
silvicultural treatment. Stocking levels show stand densities that
theoretically optimize some management objective (that is, volume
or quality production under specific economic constraints), but
they say nothing about the feasibility or operability of the treat-
ment. Professional judgment still must be exercised when the im-
plications of that judgment have become clear.

As was pointed out by Leak (1981), we must continue to evalu-
ate the recommended stocking levels to see if they satisfy the de-
sired management objective. Not meeting the objective does not
destroy the usefulness of the entire concept, but it does suggest
that refinements are needed in the stocking level or the recom-
mended relative stand density. It is only through such evaluations
that the stocking guides can be improved.

7

Literature Cited

Bickford. C. Allen and others. Stocking, normality, and measurement of
stand density. Journal of Forestry. 55: 99-104; 1957.

Braathe. Peder. Thinnings in even-aged stands: A summary of European
literature. Fredericton, NB: University of New Brunswick: 1957;
Univ. New Brunswick Bull., 92 p.

Chisman, H. H.; Schumacher. F. X. On the tree-area ratio and certain of
its applications. Journal of Forestry. 38: 311-317; 1940.

Curtis. Robert O. Stand density measures: An interpretation. Forest Sci-
ence. 16: 403-414: 1970.

Curtis, Robert O. A tree area power function and related stand density
measures for Douglas-fir. Forest Science. 17: 146-159: 1971.

Curtis, Robert O. A simple index of stand density for Douglas-fir. Forest
Science. 38: 92-94; 1982.

Drew, T. John; Flewelling, James W. Some recent Japanese theories of
yield-density relationships and their application to Monterey pine plan-
tations. Forest Science. 23: 517-534: 1977.

Drew. T. John; Flewelling, James W. Stand density management: an alter-
native approach and its application to Douglas-fir plantations. Forest
Science. 25: 518-532; 1979.

Ginrich [Gingrich], Samuel F. Measuring and evaluating stocking and
stand density in upland hardwood forests in the central states. Forest
Science. 13: 38-53; 1967.

Krajicek, John E.; Brinkman, Kenneth A.; Gingrich. Samuel F. Crown
competition — a measure of density. Forest Science. 7: 35^t2; 1961.

Leak, William B. Do stocking guides in the Eastern United States relate to
stand growth? Journal of Forestry. 79: 661-664: 1981.

Leak, William B.; Solomon, Dale S.; Filip, Stanley M. A silvicultural
guide for northern hardwoods in the Northeast. Res. Pap. NE-143.
Upper Darby, PA: U.S. Department of Agriculture, Forest Service,
Northeastern Forest Experiment Station; 1969. 34 p.

MacLean, Colin D. Relative density: the key to stocking assessment in re-
gional analysis — a forest survey viewpoint. Gen. Tech. Rep.
PNW-78. Portland, OR: U.S. Department of Agriculture, Forest
Service, Pacific Northwest Forest and Range Experiment Station:
1979. 5 p.

Myers. Clifford A. Growing stock levels in even-aged ponderosa pine.
Res. Pap. RM-33. Fort Collins, CO: U.S. Department of Agriculture.
Forest Service, Rocky Mountain Forest and Range Experiment Sta-
tion; 1967. 8 p.

Reineke, L. H. Perfecting a stand-density index for even-aged forests.
Journal of Agricultural Research. 46: 627-638: 1933.

Reukema, Donald L.; Bruce, David. Effects of thinning on yield of
Douglas-fir: concepts and some estimates obtained by simulation.
Gen. Tech. Rep. PNW-58. Portland, OR: U.S. Department of Agri-
culture, Forest Service, Pacific Northwest Forest and Range Experi-
ment Station; 1977. 36 p.

Roach, Benjamin A. A stocking guide for Allegheny hardwoods and its use
in controlling intermediate cuttings. Res. Pap. NE-373. Broomall.
PA: U.S. Department of Agriculture, Forest Service, Northeastern
Forest Experiment Station; 1977. 30 p.

Rogers, Robert. Evaluating stocking in upland central hardwood forests
using metric measurements. Res. Pap. NC-187. St. Paul, MN: U.S.
Department of Agriculture, Forest Service. North Central Forest Ex-
periment Station; 1980. 5 p.

Society of American Foresters. Terminology of forest science, technology
practice and products. Ford-Robertson. F.C., ed. Washington. DC:
Society of American Foresters; 1971. 345 p.

U.S. Department of Agriculture. Forest Service. The principal laws

relating to Forest Service activities. Agric. Handb. 453. Washington.
DC: U.S. Department of Agriculture: (rev.) 1983. p. 441^160.

West. P. W. Comparison of stand density measures in even-aged regrowth
eucalypt forest of southern Tasmania. Canadian Journal of Forest Re-
search. 13: 22-31; 1982.

8